Pressure change with constant volume

  • Thread starter SadStudent
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  • #1

Homework Statement


Given two moles of some gas with two atoms per molecule which has energy [itex]U=aK_{B}T[/itex].
Assume the initial pressure is [itex]P_{i}= 2[/itex] Atm and the initial volume is [itex]P_{i}= 0.001\ m^{3}[/itex].
Now we heat it in an isochoric process to [itex]2P_{i}[/itex].

What would be [itex]\Delta T[/itex]?
What would be the work required to do that?
What would be the change in the gas particles' internal energy?

Homework Equations


[itex]U=aK_{B}T[/itex]
[itex]dU=PdS-TdV[/itex]

The Attempt at a Solution


Well using the first law of thermodynamics, I got that under constant volume [itex]dV=0[/itex] so [itex]\frac{dQ}{dT}=\frac{\partial U}{\partial T}[/itex] so the entire energy that we spent on heating would be transferred into the gas.
What's a tricky to me is to formulate the change in temperature as a function of pressure because [itex]dV=0[/itex] so I'd really welcome a hint.

Thanks!
 
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Answers and Replies

  • #2
TSny
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Homework Equations



[itex]dU=PdS-TdV[/itex]

Oops, check that.

What's a tricky to me is to formulate the change in temperature as a function of pressure because [itex]dV=0[/itex] so I'd really welcome a hint.

Can you assume the gas obeys the ideal gas law?
 
  • #3
Oops, check that.


Can you assume the gas obeys the ideal gas law?

And yes of course it was a typo :) it's supposed to be [itex]dU=TdS-PdV[/itex]

I'm really not sure whether I can, is there a way of solving this without this assumption?
 
Last edited:

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